Adaptive detector arrays for optical communications receivers

ABSTRACT

An optical communications receiver comprising a wide-band optical detector array and a high-speed digital signal processor programmed to operate on the raw data from the detector array to ameliorate the effects of atmospheric turbulence on the performance of the optical receiver in real-time while operating within the terrestrial atmosphere, or while attempting to communicate through any similar turbulent medium is provided. A method of sending optical communications through such optical communications receivers is also provided.

CROSS-REFERENCE TO RELATED APPLICATION(S)

[0001] This application claims the benefit of U.S. provisionalapplication No. 60/253,610 filed on Nov. 28, 2000, the content of whichis incorporated herein by reference.

FIELD OF THE INVENTION

[0002] This invention is directed to improved optical receivers, andparticularly to high data-rate optical receivers utilizing wide-bandoptical detector arrays capable of correcting for signal degradationcaused by atmospheric turbulence.

BACKGROUND OF THE INVENTION

[0003] It is well known that ground-based reception of optical signalssuffers from degradation of the optical phase-front caused byatmospheric turbulence. This turbulence leads to a reduction in theeffective diameter of the receiving telescope, and to randomfluctuations of the receiver's “point spread function” (PSF) in thefocal plane.

[0004] For example, the diffraction-limited field of view (FOV) of areceiving telescope can be taken to be approximately θ_(dl)≅λ/D_(R),which, for a 3-m aperture and 1 μm wavelength, translates to 0.33 μrad.If the effective focal length of the telescope is 6 m (implying an F/2instrument), then a diffraction-limited PSF of 2 μm diameter, or 0.002mm, will be produced in the focal plane. Thus, under ideal conditions avery small detector could be used to collect virtually all of the signalenergy, while at the same time spatially filtering out most of thebackground radiation.

[0005] However, atmospheric conditions rarely permit diffraction-limitedoperation of large telescopes; even under “good” nighttime seeingconditions, the phase of the received signal field tends to becomeuncorrelated over distances greater than 20 cm, deteriorating to aslittle as 2 to 4 cm during the day. Under these conditions, thedimensions of the PSF in the focal-plane tends to increase inverselywith coherence length, as if the diffraction-limited telescope werecorrespondingly reduced; the telescope still collects all of the signalenergy propagating through its physical aperture, but the collectedsignal energy is redistributed into a much larger spot in the focalplane. In conventional receivers, the receiver's FOV is increasedproportionally to collect the signal. However, this increase in thereceiver's FOV leads to a corresponding increase in the amount ofinterfering background radiation offsetting much of the performancegain.

[0006] Some attempts have been made to utilize signal-processinghardware to reduce the deleterious effects of atmospheric turbulence onreceiver performance. However, due to the limitations of the chosenalgorithms and the electronics utilized, only the average PSF of thereceived signals over a relatively long time period have beensuccessfully processed. Although some performance improvement has beenseen from receivers utilizing these time-average PSF signal-processingtechniques, because the PSF can change on the order of milliseconds muchof the detailed information from the processed transmissions is lost.

[0007] Accordingly, there is a need for an optical communicationsreceiver capable of correcting the signal degradation from atmosphericturbulence instantaneously and without significantly increasinginterference from background radiation.

SUMMARY OF THE INVENTION

[0008] The present invention is directed to an optical communicationsreceiver comprising a wide-band optical detector array and a high-speeddigital signal processor assembly programmed to operate on the raw datafrom the detector array in real-time to ameliorate the effects ofatmospheric turbulence on the performance of the optical receiver whileoperating within the terrestrial atmosphere, or while attempting tocommunicate through any similar turbulent medium.

[0009] In one embodiment, the detector array is designed forcommunications applications such that the signal processing assemblyprocesses an array of parallel outputs, one from each detector element,instead of the usual serial row or column readouts typical in imagingapplications. In such an embodiment, each detector element preferablyhas a bandwidth commensurate with the data requirements. Any paralleloutput detector array may be utilized in such an embodiment, such as,for example, an array of photo-multiplier tubes (PMTs) capable ofcounting individual photons or an array of “avalanche photodiode” (APD)detectors with individually accessible outputs.

[0010] In one embodiment, the signal processing assembly samples eachoutput from the detector array at the Nyquist rate, and uses thesesamples to measure the average signal and background noise energies overeach detector element. In such an embodiment, since the coherence timefor the turbulence-degraded fields is on the order of severalmilliseconds, the integration time for this measurement can last up to amillisecond or more, during which time a great many data-symbols arereceived.

[0011] In the above embodiments, several possible algorithms can beapplied via the signal processing assembly to combine the detectoroutputs advantageously, i.e., to maximize the probability of correctdetection. For example, in one embodiment, a logarithmic function of theratio of signal and noise energies is applied to each output for a shorttime corresponding to the coherence-time of the channel. In analternative embodiment, a time-varying “mask” is computed and applied tothe array such that only those elements of the array with the greatestsignal content are utilized.

[0012] In still yet another embodiment, the invention is directed to amethod of ameliorating the effects of atmospheric turbulence on theperformance an optical receiver utilizing the detector array and signalprocessing assembly described herein.

BRIEF DESCRIPTION OF DRAWINGS

[0013] These and other features and advantages of the present inventionwill be better understood by reference to the following detaileddescription when considered in conjunction with the accompanyingdrawings wherein:

[0014]FIG. 1a is a representation of a receiver's point spread functionunder ideal conditions;

[0015]FIG. 1b is a representation of a receiver's point spread functionunder atmospheric turbulence conditions;

[0016]FIG. 2 is a schematic of an optical receiver according to thepresent invention;

[0017]FIG. 3 is a flowchart of an embodiment of a signal processingmethod utilized in the optical receiver according to the presentinvention;

[0018]FIG. 4 is a representation of a receiver's point spread functionoverlaid with a signal mask by a signal-processing assembly according tothe present invention;

[0019]FIG. 5 is a graphical representation of the performance of anoptical receiver according to the present invention in terms of averagenumber of received photons;

[0020]FIG. 6 is a graphical representation of the performance of anoptical receiver according to the present invention in terms of averagenumber of received photons;

[0021]FIG. 7a is a graphical representation of the performance of anoptical receiver according to the present invention in terms of photonefficiency;

[0022]FIG. 7b is a graphical representation of the performance of anoptical receiver according to the present invention in terms of photonefficiency;

[0023]FIG. 8 is a graphical representation of the performance of anoptical receiver according to the present invention in terms of numberof ranked detector elements included;

[0024]FIG. 9a is a graphical representation of the performance of anoptical receiver according to the present invention with various PPMdimensions, and background noise levels;

[0025]FIG. 9b is a graphical representation of the performance of anoptical receiver according to the present invention with various PPMdimensions, and background noise levels;

[0026]FIG. 9c is a graphical representation of the performance of anoptical receiver according to the present invention with various PPMdimensions, and background noise levels;

[0027]FIG. 9d is a graphical representation of the performance of anoptical receiver according to the present invention with various PPMdimensions, and background noise levels;

[0028]FIG. 10 is a graphical representation of the performance of anoptical receiver according to the present invention for differentrealizations of the instantaneous point spread functions;

[0029]FIG. 11 is a graphical representation of the performance of threedifferent signal-to-noise ratio measures considered in an opticalreceiver according to the present invention with;

[0030]FIG. 12 is a graphical representation of the performance usingdifferent signal-to-noise ratio measures according to the presentinvention; and

[0031]FIG. 13 is a graphical representation of the effect of real-timesignal-to-noise ratio estimations on the performance of an opticalreceiver according to the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0032] The present invention is directed to an optical communicationsreceiver comprising a wide-band optical detector array and a high-speeddigital signal processor assembly programmed to operate on the raw datafrom the detector array to ameliorate the effects of atmosphericturbulence on the performance of the optical receiver in real-time whileoperating within the terrestrial atmosphere, or while attempting tocommunicate through any similar turbulent medium.

[0033] An example of the increase in the effective dimensions of anexemplary receiver point-spread function over its diffraction-limitedvalue as a result of atmospheric turbulence is shown by comparison inFIGS. 1a and 1 b. The hypothetical signal shown in these figurescorrespond to a telescope having a 1 m aperture, an 0.3 m centralobstruction, and a 4 cm atmospheric coherence. As shown in FIG. 1a,under ideal conditions the undistorted signal generates a diffractionlimited point spread function (PSF) in the detector array. However, asshown in FIG. 1b, under the influences of atmospheric turbulence, thepoint-spread function is degraded and enlarged.

[0034] Under such conditions, in order to collect all of the signalenergy, the dimensions of a single optical detector must be made largeenough to encompass the degraded point-spread function as well as itsrandom excursions in the focal plane, which tend to change on time scaleof 10 to 100 ms. Thus, the active area of the detector must be madelarge enough to encompass most of the signal energy most of the time.However, a large detector implies a large receiver field of view, whichin turn implies a corresponding increase in the amount of backgroundradiation admitted into the receiver. That, in turn, degradescommunication performance.

[0035] Although in the above example a telescope of 1 m diameter with asecondary obstruction of 0.3 m has been assumed, it should be understoodthat similar results hold for larger telescope diameters as well as longas the focal-plane signal distribution is dominated by turbulenceeffects. Since the diffraction-limited PSF is inversely proportional tothe telescope diameter, this condition generally will be satisfied forlarger telescope diameters; however, the background and signal energiesmust be properly scaled to account for the larger collecting area. Ifthe receiver optics are not diffraction limited but have significantimperfections, generating a PSF with dimension that are comparable tothe turbulence-induce distribution, then more detailed modeling of thesignal distribution becomes necessary.

[0036] A conceptual block diagram of an optical photon-counting arrayreceiver according to the present invention is shown in FIG. 2. Thereceiver 10 consists of a collecting aperture 12 and optics 14 to focusthe collected fields onto the focal plane 16 of a detector array 18comprising a plurality of detector elements 20, such as individualphotomultiplier tubes or avalanche photodiode detectors, which respondto the impinging fields. The individual output voltage 22 from everydetector element 20 of the array 18 are converted to numeric samples,which then are operated on by a signal-processing assembly 24 thatperforms the required signal processing algorithms in order to optimizethe receiver performance in real-time.

[0037] In the above embodiments, any collecting aperture 12 capable ofcollecting optical signals from an external source and transmittingthose collected signals to the receiver optics 12 may be utilized in thecurrent invention. For example, 10 cm telescopes for terrestrialrepeaters, 5 to 10 m communication apertures, or 1 m aperture opticalcommunication telescope laboratory (OCTL) receivers.

[0038] Likewise, any optics package 14 suitable for focusing thecollected fields onto the focal plane 16 of the detector array 18 may beutilized in the current invention.

[0039] Although the above embodiment only describes the use ofphotomultiplier and avalanche photodiode detector elements 20, anysuitable optical detector may be utilized in the current invention. Forexample, even PIN diode arrays could be utilized when adequate signalenergy is available.

[0040] The signal processing assembly 24 of the current invention maycomprise any electronic components suitable to allow signal analysis tooccur at sufficiently high-speed to allow instantaneous or real-timeanalysis of the PSF, i.e., which allows signal processing of eachdetector element output at the Nyquist rate not at a signal averagedrate. For example, high-speed digital signal processors (DSPs), FPGAs,or dedicated ASIC designs could be utilized.

[0041] The signal-processing assembly 24 optimizes the receiverperformance by selecting which elements 20 of the detector array 18should be used to collect data at any arbitrary instantaneous point oftime. Data from detector elements 20 with signal content sufficientlyover the background signal level to improve the signal statistics arethen combined and data from elements 20 with signal levels at or nearthe background signal level are rejected and the result is output by thesignal-processor assembly 24 to a decoder 26 which detects the incomingsignal at that arbitrary time point from the signal-processor assemblyoutput.

[0042]FIG. 3 depicts a flow-chart of an embodiment of the processutilized by an exemplary signal-processor assembly 24 according to thecurrent invention to optimize the receiver performance. Duringoperation, the signal-processor assembly 24 first obtains a vector arrayof data outputs from the detector array 18 at Step 1 and then at Step 2operates to sample the data to measure the background and signal noiseenergies and then compute an estimate of the signal intensity and a dataweighting parameter for each output based on one of several possibleprocessing algorithms to increase the probability of correct signaldetection. At Step 3, the detector outputs are multiplied by theircorresponding calculated data weighting parameter and outputs theweighted data. At Step 4 the combined weighted data is utilized todetect the transmitted signal and the signal is output to the user atStep 5.

[0043] Any data weighting algorithm and parameter may be utilized tooptimize the signal received by the processor 24 from the detector array18, such as, for example, applying a logarithmic function of the ratioof signal and noise energies to each output for a short timecorresponding to the coherence-time of the channel, or alternatively,computing and applying a time-varying “mask” to the array thateffectively uses only those elements of the array with the greatestsignal content. These exemplary algorithms and the signal-processingmethod utilized in the current invention, and schematically shown inFIG. 3 are described in greater detail below.

[0044] In a conventional single-detector element receiver, the receivermeasures the number of photons contained in a received field byproducing a stream of free electrons at its output terminal in responseto the absorbed photons. If the occurrence time of each pulse can bemeasured, and if the amplitude of each pulse is normalized to unity,then the count record consists of positive integer-valued jumpsoccurring each time a photon is detected. Therefore, the count record orcount accumulator function is a monotonically increasing function thatcontains all of the information present in the detection process and theconditional density of the total number of counts, N, given an intensityfunction λ(t), can be expressed as: $\begin{matrix}{p\left\lbrack {\left. {{N(t)}{{{\lambda (t)};{0 \leq t < T}}}} \right\rbrack = {\exp \left( {- {\int_{0}^{T}{{\lambda (t)}\quad {t}}}} \right)}} \right.} & \text{(1a)}\end{matrix}$

[0045] where N(T)=0, and $\begin{matrix}{{p\left\lbrack {{N(t)}{{{\lambda (t)};{0 \leq t < T}}}} \right\rbrack} = {\left\lbrack {\prod\limits_{i = 0}^{N}\quad {\lambda \left( w_{i} \right)}} \right\rbrack {\exp \left( {- {\int_{0}^{T}{{\lambda (t)}\quad {t}}}} \right)}}} & \text{(1b)}\end{matrix}$

[0046] where N(T)≧1. Where the set {w_(i)} represents the occurrencetimes of the detected pulses; N(t) is called the count accumulatorfunction of the process over the time interval (0,T); andλ(t)=∫∫_(A)dxdyλ(x,y;t), where A is the detector area and λ(xy;t) is theintensity process over space and time.

[0047] However, this expression only describes the output of a singledetector element responding to an optical intensity. When an array ofdetectors is used to detect the optical field, Equations 1a and 1b mustbe generalized to enable an unambiguous description of the output ofeach detector element 20.

[0048] Consider a rectangular array of detector elements 18 of K×Ldetector elements 20, as shown in FIG. 2. For some applications, such asfinding the center of the signal intensity distribution, it is importantto know the location of each detector element within the array. In suchan embodiment, the subscripts mn, where 1≦m≦K and 1≦n≦L to denote theposition of the detector element within the array. Thus, the samplefunction density defined in Equation 1 can be written as:

p[N _(mn)(t)|λ_(mn)(t);0≦t≦T](2)

[0049] which now represents the output of a particular element of thearray. Note in such an embodiment, λ_(mn)(t) can be viewed as thatportion of a spatially distributed intensity function intercepted by themnth detector element according to: $\begin{matrix}{{\lambda_{mn}(t)} = {\int_{A_{mn}}{\int{{x}{y}\quad {\lambda \left( {x,{y;t}} \right)}}}}} & (3)\end{matrix}$

[0050] where A_(mn) is its effective area. Note that if the spatialintensity distribution is known, and the location and size of eachdetector element also are known, then conditioning on the spatialintensity distribution is equivalent to conditioning on the array ofintensity components, each of which is still a function of time.Assuming that each array element observes the sum of a signal field plusmultimode Gaussian noise field with average noise count per mode muchless than one, the array outputs can be modeled as conditionallyindependent Poisson processes, conditioned on the average signalintensity over each detector element. Hence, the joint conditionalsample function density of the array can be denoted as: $\begin{matrix}{p\left\lbrack {\left. {{N(t)}{{{\lambda (t)};{0 \leq t \leq T}}}} \right\rbrack = {\prod\limits_{m = 1}^{K}\quad {\prod\limits_{n = 1}^{L}\quad {p\left\lbrack \left. {{N_{mn}(t)}{{{\lambda_{mn}(t)};{0 \leq t < T}}}} \right\rbrack \right.}}}} \right.} & (4)\end{matrix}$

[0051] where N(t)≡(N₁₁(t),N₁₂(t), . . . , N_(KL)(t)) and each componenton the right-hand side of Equation 4 is defined in Equation 1.

[0052] Accordingly, a signal propagating through the atmosphere andthrough the receiving optics 12 is transformed into a space-timeintensity function in the detector plane. The receiver 10 also collectsbackground energy from all directions, which is assumed to contribute anadditional constant intensity, λ_(b) per detector element. Theintegrated intensity is then given by Equation 3, above plus theadditional constant background level.

[0053] Once the total intensity is measured by the detector thesignal-processor operates on the signal to instantaneously determine theinformation contained therein. To accomplish this signal processing, inone embodiment, at the end of T sec, the signal processor assemblyestimates the signal intensity and then computes the probability ofhaving received the observed array of count accumulator functions andselects that message corresponding to the greatest probability of havingbeen received. The spatial component of the process typically consistsof calculating the greatest log-likelihood function, Λ(T), having aspatial portion given by an equation of the form: $\begin{matrix}{{\Lambda (T)} = {\sum\limits_{m = 1}^{K}\quad {\sum\limits_{N = 1}^{L}\quad \left\{ {\sum\limits_{({{observational}\quad {interval}})}{{\ln \left( {1 + \frac{\lambda_{s,{mn}}}{\lambda_{b}}} \right)}N_{mn}}} \right\}}}} & (5)\end{matrix}$

[0054] where N_(mn) is the total number of photons occurring over themnth detector element. It should be noted that the log-likelihoodfunction of Equation 5, above, mathematically relates only the spatialportion of the function and that such a function may require anadditional modulation dependent term. In addition, the spatial intensitymust be estimated often enough to capture any fluctuations in themodulation, but must be averaged over sufficient time to ensure adequatesignal statistics (in most cases˜msec). Rewriting the logarithmicfunctions or weights in Equation 5 as μ_(mn), allows the log-likelihoodfunction to be rewritten as: $\begin{matrix}{{\Lambda (T)} = {\sum\limits_{m = 1}^{K}\quad {\sum\limits_{N = 1}^{L}{u_{mn}N_{mn}}}}} & (6)\end{matrix}$

[0055] In this form, it is clear that the log-likelihood function iscomposed of sums of a random number of weights from each detectorelement, for example, the mnth detector element contributes an integernumber of its own weight to the sum.

[0056] According to the preceding analysis, in a receiver systemaccording to this invention, elements of the detector array containingmuch more background than signal intensity do not contributesignificantly to the error probability, since the output of thesedetector elements is multiplied by weights that are close to zero.Accordingly, in an alternative embodiment of the signal processingassembly 24 the processor first ranks the detector elements, startingwith the one containing the most signal energy and followed by everyother detector ordered according to decreasing signal intensity. Theprocessor then computes the probability of error for the first detectorelement plus background; then for the sum of the signal energies fromthe first two detector elements (plus background for the two detectorelements), and so on, until the minimum error probability is reached. Insuch an embodiment, each set of detectors may be considered to be asingle detector, so that no weighting is applied to account forvariations in the signal distribution over the detector elementsincluded in that set. The set of detector elements that achieves theminimum probability of error is the best synthesized single detectormatched to the signal-intensity distribution and is the one chosen asthe signal.

[0057] However, it should be understood that the above system requiresintensive calculations. Accordingly, in one alternative embodiment, thelogarithmic weights are partitioned into two classes: large weights areassigned a value of “1” and small weights are assigned a value “0.”Effectively, such a signal-processing method creates a “signal mask”that groups a set of the highest ranked detector elements together intoa synthesized single detector as shown schematically in FIG. 4. In turnthis synthesized detector changes with the changing channel.

[0058] Although only a binary approximation has been discussed above,any other suitable approximation could be applied to the logarithmicrates. For example, the computation of log(1+x) could be replaced by thecomputation of “x” in some cases, namely when the signal-to-noise ratioover each detector element is small.

[0059] Because computing the error probability for each increasingsubarray requires a great deal of computation time, particularly whenlarge detector arrays are used, in an alternative embodiment of theinvention, the calculation takes into account the number of detectorsand the total average signal and background energies. Utilizing such amethod three different computations analogous to signal-to-noise ratios(SNR) were created according to: $\begin{matrix}{{{SNR}_{1}(l)} = \frac{\left( {\sum\limits_{i = 1}^{l}\quad {\lambda_{s,{mn}}\tau}} \right)^{2}}{l\quad \lambda_{b}\tau}} & (7) \\{{{SNR}_{2}(l)} = {\frac{\left( {\sum\limits_{i = 1}^{l}\quad {\lambda_{s,{mn}}\tau}} \right)^{2}}{{l\quad \lambda_{b}\tau} + {\sum\limits_{i = 1}^{l}\quad {\lambda_{s,{mn}}\tau}}}\quad {and}}} & (8) \\{{{SNR}_{3}(l)} = \sqrt{\frac{4{\sum\limits_{i = 1}^{l}\quad {\lambda_{s,{mn}}\tau}}}{{2l\quad \lambda_{b}\tau} + 1}}} & (9)\end{matrix}$

[0060] where the index l represents the number of detector elements overwhich these functions are a maximized, 1≦l≦256 for the current example.

[0061] Although the above signal processing method and apparatus may beutilized with any intensity modulation technique, such as for example,binary PPM and on-off keying, in an exemplary embodiment the techniquewill be modeled on a M-ary PPM technique.

[0062] In M-ary PPM modulation, a signal pulse of duration τ sec istransmitted in one of M consecutive time slots, resulting in a PPMsymbol of duration T=τM sec. Under the hypothesis that the signal pulseis contained in the ith time slot, the signal intensity is given by:$\begin{matrix}{{\lambda^{(i)}(t)} = \left\{ \begin{matrix}{{\lambda_{s}(t)}:} & {{\left( {i - 1} \right)\tau} \leq t \leq {i\quad \tau}} \\{\quad {0:}} & {else}\end{matrix} \right.} & (10)\end{matrix}$

[0063] As before, after propagating through the atmosphere and throughthe receiving optics, this temporal intensity function is transformedinto a space-time intensity function in the detector plane. Theintegrated intensity over the mnth detector according to Equation 3 canthen be designated as λ^((i)) _(mn)(t) in order to incorporate thehypothesis dependence. Where the integrated intensity can be written as:$\begin{matrix}{{\lambda_{mn}^{(i)}(t)} = \left\{ \begin{matrix}{{\lambda_{s,{mn}}(t)} + {\lambda_{b}:}} & {{\left( {i - 1} \right)\tau} \leq t \leq {i\quad \tau}} \\{{\lambda_{b}:}\quad} & {\quad {else}}\end{matrix} \right.} & (11)\end{matrix}$

[0064] In this exemplary embodiment, it is assumed that each of the Mmessages is equally likely to be transmitted with probability M⁻¹, andthat each message generates a unique vector of detector arrayintensities at the receiver, denoted by λ^((i))(t)=(λ^((i)) ₁₁(t),λ^((i)) ₁₂(t), . . . , λ^((i)) _(KL)(t), . . . , λ^((i)) _(KL)(t). Asbefore, at the end of T sec, the signal-processing assembly computes theprobability of having received the observed array of count accumulatorfunctions and selects the message corresponding to the greatestprobability of having been received. Equivalently, the decoder selectsthe message corresponding to the greatest log-likelihood function,Λ_(i)(T), evaluated after T sec and conditioned upon the signaloccurring at the ith time-slot: $\begin{matrix}\begin{matrix}{{\Lambda_{i}(T)} = \quad {\ln \left\{ \left. \left. {p\left\lbrack {{N(t)}{{{\lambda^{(i)}(t)};{0 \leq t < T}}}} \right.} \right\rbrack \right\} \right.}} \\\left. {= \quad {\sum\limits_{m = 1}^{K}\quad \left. {{{{\sum\limits_{n = 1}^{L}\quad {\ln \left\{ {p\left\lbrack {N_{mn}(t)} \right.} \right.}}}{\lambda_{mn}^{(i)}(t)}};{0 \leq t < T}} \right\rbrack}} \right\} \\{= \quad {\sum\limits_{m = 1}^{K}\quad {\sum\limits_{n = 1}^{L}\left( {{- {\int_{{({i - 1})}\tau}^{i\quad \tau}{{\lambda_{mn}^{(i)}(t)}{\partial t}}}} + {\sum\limits_{w_{j,{mn}}\varepsilon({{{({i - 1})}\tau},{i\quad \tau}}}{\ln \quad {\lambda_{mn}^{(i)}\left( w_{j,{mn}} \right)}}} +} \right.}}} \\{\quad \left( {{terms}\quad {that}\quad {depend}\quad {only}\quad {on}\quad \lambda_{b}} \right)}\end{matrix} & (12)\end{matrix}$

[0065] where w_(j,mn) is the occurrence time of the jth photon over themnth detector element within the same time slot.

[0066] Assuming constant signal intensity over the ith slot, independentof the value i, and ignoring the terms that depend only on λ_(b) (whichhence do not convey any information about the transmission), thelog-likelihood function reduces to: $\begin{matrix}{{\Lambda_{i}(T)} = {\sum\limits_{m = 1}^{K}{\sum\limits_{n = 1}^{L}{{\ln \left( {1 + \frac{\lambda_{s,{m\quad n}}}{\lambda_{b}}} \right)}N_{m\quad n}^{(i)}}}}} & (13)\end{matrix}$

[0067] where N^((i)) _(mn) is defined as the total number of photonsoccurring over the mnth detector element during the ith time slot. Notethat in this exemplary embodiment, with constant signal intensities theactual arrival times of photons within each time slot do not contributeto the decision; hence, only the total number of detected photons,N^((i)) _(mn), matters. Given that the intensity over each detectorelement is known, the ith log-likelihood function consists of the sum ofa logarithmic function of the ratio of signal and background intensitiesfrom all detector elements over the ith pulse interval, multiplied bythe total number of detected photons; the optimum detection strategy isthen to select the symbol corresponding to the greatest log-likelihoodfunction.

[0068] In such an M-ary PPM system, two distinct cases arise, whensignal is present and when signal is not present. When signal is presentthen the intensity over the mnth element of the detector array is equalto the sum of the signal intensity λ_(mn) and the background intensityλ_(b), whereas when signal is not present the intensity over eachdetector element is simply equal to the background λ_(b).

[0069] In such a M-ary PPM system, the received information is processedand decoded correctly if the weighted sum for the signal slot (q)exceeds the weighted sum for every other, i.e., non-signal slot, suchthat:

Λ_(q)(T)>Λ_(i)(T)   (14)

[0070] However, since the weights for each log-likelihood function arethe same, it is possible that the maximum sum of weights occurs over twoor more times, one of which is the true signal time, creating a “tie.”In the case of a “tie” for the largest weighted sum in such a system,random choice is utilized among the largest likelihood functions: ifthere are r nonsignal slots tied for biggest with the correct signalslot, then the probability of selecting the correct symbol in thepresence of (r+1) ties for biggest is (r+1)⁻¹. However, there are, (M−1)taken r at a time, ways these ties can occur among M slots. On the otherhand, if none of the detectors registers a photon over any of the Mslots, then we have to make a random choice among M possibilities, whichyields a correct decision with probability M⁻¹. Assuming equiprobablesignals, the probability of correctly decoding the received signal isdenoted in Equation 15, below. $\begin{matrix}{{P_{M}(C)} = {{P_{M}\left( C \middle| H_{q} \right)} = {\left\{ {\sum\limits_{r = 0}^{M - 1}{\left( \frac{1}{r + 1} \right)\left( \frac{M - 1}{r} \right){\sum\limits_{k = 1}^{\infty}{{{p_{q}\left( \alpha_{k} \middle| H_{q} \right)}\left\lbrack \underset{i \neq q}{p_{i}\left( \alpha_{k} \middle| H_{q} \right)} \right\rbrack}^{r}\left\lbrack \underset{i \neq q}{\sum\limits_{j = 0}^{k - 1}{p_{i}\left( \alpha_{j} \middle| H_{q} \right)}} \right\rbrack}^{M - 1 - r}}}} \right\} + {M^{- 1}\left\{ {{p_{q}\left( \alpha_{0} \middle| H_{q} \right)}\left\lbrack {p_{i}\left( \alpha_{0} \middle| H_{q} \right)} \right\rbrack}^{M - 1} \right\}}}}} & (15)\end{matrix}$

[0071] where p_(q) and p_(i), i≠q, refer to the probability densitiescorresponding to the signal and non-signal hypotheses, respectively.

[0072] Alternatively, counting all “ties” as errors yields a tight lowerbound on the probability of correct detection, and yields an easier tocalculate probability function: $\begin{matrix}{{P_{M}(C)} \geq {P_{M}^{1}(C)} \equiv {{\sum\limits_{k = 1}^{\infty}{{p_{q}\left( \alpha_{k} \middle| H_{q} \right)}\left\lbrack \underset{i \neq q}{\sum\limits_{j = 0}^{k - 1}{p_{i}\left( \alpha_{j} \middle| H_{q} \right)}} \right\rbrack}^{M - 1}} + {M^{- 1}\left\{ {{p_{q}\left( \alpha_{0} \middle| H_{q} \right)}\left\lbrack {p_{i}\left( \alpha_{0} \middle| H_{q} \right)} \right\rbrack}^{M - 1} \right\}}}} & (16)\end{matrix}$

[0073] In turn this lower bound on the probability of correct detectionyield the following upper bound on the error probability, which may beutilized to evaluate a variety of proposed detector array schemes:

P ^(μ) _(M)(E)≡1−P ¹ _(M)(C)≧P_(M)(E)   (17)

[0074] Although the above analysis has assumed an optimal detectorregime, such a M-ary PPM system might also use a suboptimal or adaptivesynthesized single detector, as described above. In such an embodiment,the probability of correct detection can be obtained directly fromEquation 15, by setting α_(k)=k in the probability densities andassuming constant signal and background intensities over each time slot,yielding: $\begin{matrix}{{{p_{q}\left( k \middle| H_{q} \right)} = {\frac{\left( {{\lambda_{s}\tau} + {\lambda_{b}\tau}} \right)^{k}}{k!}e^{- {({{\lambda_{s}\tau} + {\lambda_{b}\tau}})}}}}{and}} & (18) \\{{p_{i}\left( k \middle| H_{q} \right)} = {\frac{\left( {\lambda_{b}\tau} \right)^{k}}{k!}e^{{- \lambda_{b}}\tau}}} & (19)\end{matrix}$

[0075] Direct substitution of these Poisson densities into Equation 15yields a probability of correct detection according to: $\begin{matrix}{{P_{M}(C)} = {\left\{ {\sum\limits_{r = 0}^{M - 1}{\left( \frac{1}{r + 1} \right)\left( \frac{M - 1}{r} \right){\sum\limits_{k = 1}^{\infty}{\frac{\left( {{\lambda_{s}\tau} + {\lambda_{b}\tau}} \right)^{k}}{k!}{{e^{- {({{\lambda_{s}\tau} + {\lambda_{b}\tau}})}}\left\lbrack {\frac{\left( {\lambda_{b}\tau} \right)^{k}}{k!}e^{{- \lambda_{b}}\tau}} \right\rbrack}^{r}\left\lbrack {\sum\limits_{j = 0}^{k - 1}{\frac{\left( {\lambda_{b}\tau} \right)}{j!}e^{{- \lambda_{b}}\tau}}} \right\rbrack}^{M - 1 - r}}}}} \right\} + {M^{- 1}e^{{- {({\lambda_{s} + {M\quad \lambda_{b}}})}}\pi}}}} & (20)\end{matrix}$

[0076] However, when the array contains a large number of detectorelements, the computation of the probability density of the weighted sumof Poisson random variables by the signal processing assembly may becomeprohibitive. In such a case, an alternative approximating signalprocessing method may be utilized to substitute the true discretedensity with a simpler continuous density. For example, in onealternative exemplary embodiment, a Gaussian approximation to thediscrete density of the weighted sum of Poisson random variables isderived from the characteristic function of the discrete density.

[0077] The various signal processing techniques detailed above weremodeled utilizing an exemplary M-ary pulse-position modulation (PPM)data transmission protocol. In this protocol one of M intensityfunctions is received by the receiver 10 and the receiver attempts todetermine the correct symbol based on observations of the array of countaccumulator functions over each of M time slots. It is assumed for thepurpose of this exemplary embodiment that the symbol boundaries areknown and that the arrival time of each detected photon and total numberof detected photons can be stored for a limited duration of timenecessary for processing by the signal-processing assembly 24.

[0078] First, a comparison of the performance of signal-processingassemblies utilizing the optimally weighted array receiver and theadaptive synthesized single-detector signal-processing methods describedabove, were carried out for two model receivers exposed to averagebackground energies of K_(b)≡λ_(b)τ=0.1 and 1.0.

[0079] Two different signal models were used: 1) a simple test modelwherein only 5 of the 16×16=256 total detector elements were assumed tocontain signal energy while the rest were assumed to contain no signal;and 2) a more realistic 16×16 detector array model wherein the signaldistribution over the array was simulated using a Kolmogorov turbulencemodel in which all 256 detector elements potentially contained somesignal.

[0080] For the test model, the proportions of the total average absorbedsignal energy, K_(s)≡λ_(s)τ, over the five detector elements wereassumed to be (1.0, 0.3, 0.2, 0.05, 0.02). The optimally weighted arrayreceiver (Equation 16) and the synthesized single-detector receiver(Equation 20) signal processing methods were then evaluated with thismodel and compared with results obtained via Monte Carlo simulations.The results are shown in FIG. 5, as a function of the total averageabsorbed signal energy, K_(s). From this plot, it is evident thatoptimal weighting yields somewhat better performance than the suboptimumsingle-synthesized or signal mask array, and that greater improvementsoccur at greater background intensities. However, the improvements dueto the more complicated signal-processing utilized in the optimallyweighted array are only about 0.3 dB at an error probability of 0.001for the high background case.

[0081] In FIG. 6, a realistic spatial distribution of the signalintensity over the focal plane was generated using Kolmogorov phasescreens. Monte Carlo simulations were performed to evaluate the errorprobability for the optimally weighted array. The Gaussian approximationto the error probability defined by: $\begin{matrix}{{\eta = {\sum\limits_{m = 1}^{K}{\sum\limits_{n = 1}^{L}{\mu_{m\quad n}\lambda_{m\quad n}\tau}}}}{and}} & (21) \\{\sigma^{2} = {\sum\limits_{m = 1}^{K}{\sum\limits_{n = 1}^{L}{\mu_{m\quad n}^{2}\lambda_{m\quad n}\tau}}}} & (22)\end{matrix}$

[0082] was also evaluated for the binary PPM case, M=2, with averagebackground energies (per detector element) of K_(b)≡λ_(b)τ=0.1, 1.0 and5.0 photons/time slot, as a function of the total average signal energy.

[0083] From this plot, it can be seen that the Gaussian approximation isclose to the exact values . obtained from Monte Carlo simulation andthat good agreement is obtained even for small background energies perdetector element, as direct comparison with the simulation resultsindicates. In fact, the Gaussian approximation embodiment providesuseful results over the entire range of background and signal energiesrepresented in FIG. 6. The performance of the synthesized signal maskedprocess is also shown; it can be seen that its performance is wellwithin tolerable limits.

[0084] Both analytical calculations and Monte Carlo simulations wereperformed in order to obtain PPM error probabilities for the receiveraccording to the invention. Performance of the optimally weighted arrayreceiver embodiment was obtained from simulations; for each PPM symbol,M Poisson random variables with the proper statistics were generated,the optimum weights were applied, and the symbol corresponding to thelargest observable selected. Simulated turbulence-degraded signaldistributions were then generated over the 16×16 detector array for allsubsequent results. With no loss in generality, the transmitted symbolwas always assumed to be the one corresponding to a signal pulse in thefirst slot. The detector process was repeated a large number of times(until 100 errors were accumulated) and repeated for increasing averagesignal energy with various background levels. The results of this testare shown in FIG. 7a and 7 b for M=2, 16 and 256. The probability of biterror is shown as a function of the receiver's photon efficiency, ρ,which is a measure of the average number of bits of information carriedby each photon. It can be seen from the plot that, with backgroundlevels from 0.1 to 1.0 photons per slot, ρ from 0.3 to 0.5 bits/photoncan be achieved with 256 PPM signaling at uncoded symbol-errorprobabilities of around 0.001 to 0.01.

[0085] In order to generate a spatial distribution of the signalincident upon the detector plane, a sample field was generated using aKolmogorov phase-screen program, resulting in a matrix of complex signalamplitudes. For the simulations, an atmospheric correlation length ofr₀=4 cm was assumed, which implies that the results should apply to anyreceiving aperture that is much greater than this correlation length.The field intensity generated in the detector plane by the simulationthen was integrated over the elements of a 16×16 detector array, whichwas assumed to encompass the extent of the signal distribution in thedetector plane. The detector signal intensities are normalized so thatfor the mnth detector an average number of absorbed signal photon ofλ_(s,mn)τ is obtained. A constant average background photon energy ofλ_(b)τ is assumed over each detector element.

[0086] For a given sample function of the intensity distribution, the256 detector elements were sorted in decreasing order of average signalenergy, and Mary PPM symbol-error probabilities were calculated forincreasing numbers of detectors, starting with the first detector, usingthe synthesized single-detector signal processing embodiment of thecurrent invention. FIG. 8 shows the symbol-error probability for binaryPPM, M=2, as a function of the number of detector elements used for thecase K_(s)=10 and K_(b)=0.1 (that is, the total average signal photonsabsorbed by the entire array is 10 and the average number of backgroundphotons per detector element is 0.1.) It can be seen from the plot that,for this case, the smallest error probability of 0.0049 is achieved byassigning unity weight to the first 11 detector elements containing thegreatest signal intensities and zero to all the rest.

[0087] In FIGS. 9a and 9 b, binary PPM symbol-error probabilities areshown as a function of total average number of absorbed signal photonsfor four cases: 1) when the optimum number of unweighted detectorelements is used, 2) when the optimally weighted array is simulated, 3)when all 256 detector elements are given unity weight (synthesizing alarge, nonadaptive single-detector element), and 4) when an idealadaptive optics system succeeds in concentrating all of the availablesignal energy into a single detector element, which then is the onlydetector element that is observed.

[0088] Using the same focal-plane signal distribution as before, errorprobabilities were computed for average background photon counts of 0.1and 1.0, shown in FIGS. 9a and 9 b, indicating performance gains by theadaptive detector array receiver according to the current invention overa single large nonadaptive detector of 2 and 2.8, respectively, at anerror probability of 0.001, corresponding to 3 and 4.5 dB of performanceimprovement. Meanwhile, when compared with the ideal adaptive opticsreceiver that concentrates all of the collected signal energy in asingle element of the array, the gains are 3.8 and 8.2, corresponding to5.9 and 9.1 dB of improvement. However, between the optimally weightedarray embodiment and the synthesized single detector or signal maskembodiment of the current invention, there is only a 0.3 dB improvementat a symbol error probability of 0.001, even with a relatively highbackground energy of K_(b)=1.0.

[0089] Similar gains are evident in FIGS. 9c and 9 d, which representthe symbol-error probability, P(SE), of the optimized subarray observing16-dimensional (M=16) PPM. The accuracy of the union bound evaluated forthe case λ_(b)τ>>1 is evident, especially at the lower errorprobabilities.

[0090] As shown in FIG. 10, performance improvements are also observedfor several different focal-plane distributions at an average backgroundenergy of one photon per detector per slot to verify that the aboveresults were typical. This plot shows that three out of four simulationsyielded performance comparable to that shown in FIG. 9b, requiringapproximately 26 signal photons to achieve an error probability of 0.001while utilizing 9 to 13 elements of the array in the region of errorprobabilities examined. Accordingly, receiver performance is independentof array distribution under the same atmospheric and receiverparameters.

[0091]FIG. 11 shows the three functions versus l for the case λ_(s)τ=10and λ_(b)τ=0.1, assuming Poisson statistics. As can be seen from theplot, the maximum values for these three measures are reached when lequals 10, 22, and 7 detector elements, resulting in binary PPMsymbol-error probabilities or 5.978×10⁻³, 5.84×10⁻³, and 1.049×10⁻²,respectively, as compared with the performance of the true optimumsubarray of 4.884×10⁻³ calculated from the actual error probabilitiesand achieved with 15 detector elements.

[0092]FIG. 12 in turn shows how subarrays obtained using the threedifferent SNR measures given by Equations 7, 8 and 9, respectively,compare with the performance of the true optimized subarray over a rangeof signal energies for a particular signal distribution. As can beobserved from the plot, both SNR₁ and SNR₂ yield performances comparableto that of the optimized subarray and, therefore, could be used tooptimize the subarray dimensions in real time.

[0093] Finally, thus far the above evaluations of the performance of thereceivers according to the present invention were obtained under theassumption that the true value of the average signal and backgroundphotons absorbed by each detector element are known. Accordingly, inthese tests the sorting of the detector elements is based on the truesignal energies. However, in many systems the signal energies willchange with time due to turbulence. Therefore, the case when the signalenergies were not known a priori, but had to be estimated was tested.The results of the simulations in which actual Poisson deviates weregenerated for each array element, and the mean signal energies estimatedfrom the observed outputs, are presented in FIG. 13 for binary PPM.

[0094] For each detector array element, Poisson random variable weregenerated for the Mary signal and background slots with averageintensities obtained from the Kolmogorov phase-screen output plus aspecified level of background light. These deviates were generated for LPPM symbols and the slot outputs added for each detector element,resulting in m×n statistics according to: $\begin{matrix}{Y_{m\quad n} = {\sum\limits_{i = 1}^{L}{\sum\limits_{j = 0}^{M - 1}{X_{m\quad n}\left( {i,j} \right)}}}} & (23)\end{matrix}$

[0095] where X_(mn)(i,j) is the output of the jth slot of the ith PPMsymbol. These statistics were sorted as before from largest to smallest.The average number of signal photons was estimated from these statisticsas: $\begin{matrix}{{\lambda_{s,{m\quad n}}\tau} = {\max \left( {{\frac{Y_{m\quad n}}{L} - {M\quad \lambda_{b}\tau}},0} \right)}} & (24)\end{matrix}$

[0096] where it is assumed in this exemplary embodiment that the actualbackground intensity can be estimated accurately, both because it isessentially constant and because typically there is significant deadtime between PPM symbols to allow for transmitter laser recovery, whichcan be used to estimate the background intensity accurately since nosignal photon are present. During operation once the average signal andbackground energies have been estimated, SNR₁(l) may again be maximizedover the number of elements, l, as before in order to obtain the optimumdetector subarray.

[0097] Results for binary PPM with estimated signal energies are shownin FIG. 13 for an average background energy of 1.0 photon per detectorelement per slot. This Figure shows the symbol-error probability as afunction of total average absorbed signal energy, K_(s), using estimatesof the signal intensity obtained from the simulation with L=1000, aswell as three other curves where exact knowledge of the inputdistribution was assumed; the 16×16 subarray, the optimized subarraybased on the actual energy probabilities, and the subarray obtained bymaximizing SNR₁. It should be noted that the simulation and SNR₁subarray curves are indistinguishable in both cases, indicating thatestimation of the signal energies over the array does not result in anyappreciable performance degradation. It also is evident that subarrayoptimization based on the simple SNR₁ algorithm results in only slightlosses, but succeeds in greatly reducing the complexity of theestimator; for K_(b)=1.0, the loss is less than 0.15 dB over the entirerange considered in FIG. 13.

[0098] The elements of the apparatus and method and the general featuresof the components are shown and described in relatively simplified andgenerally symbolic manner. Appropriate structural details and parametersfor actual operation are available and known to those skilled in the artwith respect to the conventional aspects of the process.

[0099] Although specific embodiments are disclosed herein, it isexpected that persons skilled in the art can and will design alternativeadaptive optical receivers that are within the scope of the followingclaims either literally or under the Doctrine of Equivalents.

What is claimed is:
 1. An optical receiver for receiving and processingturbulence degraded optical signals comprising: a detector arraycomprising a plurality of detector elements for detecting a point spreadfunction characteristic of the received optical signal, wherein each ofthe plurality of detector elements outputs a detector outputcharacteristic of a portion of the point spread function; a signalprocessor for real-time processing the detector outputs to optimize theperformance of the receiver by separating a plurality of performanceenhancing detected signals from a plurality of performance degradingdetected signals, the signal processor further comprising: a receivercircuit for receiving the detector outputs from the plurality ofdetector elements and estimating a signal intensity from each detectoroutput, a selector circuit for selecting the performance enhancingdetector outputs by selecting the detector outputs containing sufficientsignal intensity to improve the performance of the optical detector, anda combiner circuit for combining the performance enhancing detectoroutputs into a single processed signal characteristic of theinstantaneous point spread function; and a decoder for detecting thereceived optical signal in the processed signal and outputting a decodedoptically transmitted symbol to a user.
 2. An optical receiver asdescribed in claim 1 further comprising a collecting aperture forcollecting the transmitted signals from an external source.
 3. Anoptical receiver as described in claim 1 further comprising focussingoptics for focussing the received signals onto the detector.
 4. Anoptical receiver as described in claim 1 wherein the detector comprisesa grid array of N×M detector elements, where N is ≧2 and M is ≧2.
 5. Anoptical receiver as described in claim 1 wherein the detector comprisesa grid array of N×M detector elements, where N is ≧4 and M is ≧4.
 6. Anoptical receiver as described in claim 1 wherein the detector elementsare selected from the group consisting of: photomulipliers, avalanchephotodiodes and PIN diodes.
 7. An optical receiver as described in claim1 wherein the signal processor operates on the received optical signalat a rate equal to or greater than the Nyquist rate.
 8. An opticalreceiver as described in claim 1 wherein the signal processor processesthe received optical signal by weighting the detector outputs based on afunction of a characteristic signal to noise ratio wherein the functionis either a logarithmic function or an approximation of a logarithmicfunction.
 9. An optical receiver as described in claim 1 wherein thesignal processor processes the received optical signal by ranking thedetector outputs and utilizing only those detector outputs with thegreatest signal content.
 10. An optical receiver as described in claim 1wherein the received optical signal is transmitted in an intensitymodulated transmission protocol.
 11. An optical receiver as described inclaim 1 wherein the received optical signal is transmitted in a protocolselected from the group consisting of: binary pulse-position modulation,M-ary pulse-position modulation and on-off key modulation.
 12. A methodof optimizing an optical receiver comprising: detecting an incomingoptical signal with a plurality of detector elements such that eachdetector element outputs a detector output; estimating the signalintensity of each of the detector outputs; analyzing the detectoroutputs to determine which detected signals have sufficient signalintensity to improve the performance of the optical receiver; selectingthose performance enhancing detector outputs; combining the performanceenhancing detector outputs into a single processed signal; and decodingthe processed signal to determine the data content of the incomingoptical signal.
 13. A method as described in claim 12 wherein the stepof analyzing comprises calculating weighted log-likelihood functions foreach detector output and comparing the weighted log-likelihood functionsfor each detector output to determine the greatest log-likelihoodfunction.
 14. A method as described in claim 12 wherein the step ofanalyzing comprises ranking the detector outputs based on their signalintensity, and wherein the step of comparing comprises computing theprobability error for each successive set of detector elements plus ameasured background noise for each of the detector elements.
 15. Amethod as described in claim 12 wherein the step of analyzing comprisesranking the detector outputs based on their signal intensity, andwherein the step of comparing comprises assigning a weighting value of 1to those detector outputs above a specified threshold of receivedoptical signal and assigning a weighting value of 0 to those outputsbelow the specified threshold to create an effective signal mask.
 16. Amethod as described in claim 12 wherein the step of analyzing comprisesranking the detector outputs based on their signal intensity, andwherein the step of comparing comprises assigning a weighting value toeach of the detector outputs according to an approximation of alogarithmic rate for each of the detector outputs.
 17. A method asdescribed in claim 12 wherein the step of comparing comprisescalculating a signal-to-noise ratio measure for each detector output andassigning a weighting value to the outputs based on those ratios.
 18. Amethod of optimizing an optical receiver comprising: detecting anincoming optical signal with a plurality of detector elements such thateach detector element outputs a detector output; and optimizing thedetector outputs utilizing an optimally weighting signal processingmeans.
 19. A method of optimizing an optical receiver comprising:detecting an incoming optical signal with a plurality of detectorelements such that each detector element outputs a detector output; andoptimizing the detector outputs utilizing an adaptive synthesizedsingle-detector signal processing means.
 20. A method of optimizing anoptical receiver comprising: detecting an incoming optical signal with aplurality of detector elements such that each detector element outputs adetector output; and optimizing the detector outputs utilizingsignal-to-noise processing means.